Properties

Label 392.2.z.a.109.5
Level $392$
Weight $2$
Character 392.109
Analytic conductor $3.130$
Analytic rank $0$
Dimension $648$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [392,2,Mod(37,392)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(392, base_ring=CyclotomicField(42))
 
chi = DirichletCharacter(H, H._module([0, 21, 32]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("392.37");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 392 = 2^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 392.z (of order \(42\), degree \(12\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.13013575923\)
Analytic rank: \(0\)
Dimension: \(648\)
Relative dimension: \(54\) over \(\Q(\zeta_{42})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label 109.5
Character \(\chi\) \(=\) 392.109
Dual form 392.2.z.a.205.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.31212 + 0.527576i) q^{2} +(0.371894 + 2.46736i) q^{3} +(1.44333 - 1.38449i) q^{4} +(1.53857 + 0.603845i) q^{5} +(-1.78969 - 3.04127i) q^{6} +(2.53791 - 0.747686i) q^{7} +(-1.16340 + 2.57808i) q^{8} +(-3.08282 + 0.950925i) q^{9} +O(q^{10})\) \(q+(-1.31212 + 0.527576i) q^{2} +(0.371894 + 2.46736i) q^{3} +(1.44333 - 1.38449i) q^{4} +(1.53857 + 0.603845i) q^{5} +(-1.78969 - 3.04127i) q^{6} +(2.53791 - 0.747686i) q^{7} +(-1.16340 + 2.57808i) q^{8} +(-3.08282 + 0.950925i) q^{9} +(-2.33737 + 0.0193953i) q^{10} +(-0.767062 + 2.48676i) q^{11} +(3.95279 + 3.04632i) q^{12} +(6.17046 - 1.40837i) q^{13} +(-2.93558 + 2.31999i) q^{14} +(-0.917715 + 4.02077i) q^{15} +(0.166388 - 3.99654i) q^{16} +(1.72613 - 1.17685i) q^{17} +(3.54335 - 2.87415i) q^{18} +(1.99327 - 1.15081i) q^{19} +(3.05668 - 1.25859i) q^{20} +(2.78864 + 5.98386i) q^{21} +(-0.305473 - 3.66761i) q^{22} +(-4.07160 - 2.77597i) q^{23} +(-6.79371 - 1.91175i) q^{24} +(-1.66268 - 1.54274i) q^{25} +(-7.35337 + 5.10333i) q^{26} +(-0.244841 - 0.508417i) q^{27} +(2.62787 - 4.59286i) q^{28} +(-0.406906 + 0.844948i) q^{29} +(-0.917109 - 5.75991i) q^{30} +(-3.84883 + 6.66636i) q^{31} +(1.89016 + 5.33173i) q^{32} +(-6.42098 - 0.967807i) q^{33} +(-1.64401 + 2.45484i) q^{34} +(4.35624 + 0.382133i) q^{35} +(-3.13298 + 5.64063i) q^{36} +(-5.68048 + 0.425693i) q^{37} +(-2.00827 + 2.56161i) q^{38} +(5.76970 + 14.7009i) q^{39} +(-3.34674 + 3.26405i) q^{40} +(-6.63484 - 8.31983i) q^{41} +(-6.81597 - 6.38033i) q^{42} +(-4.22854 - 3.37215i) q^{43} +(2.33576 + 4.65119i) q^{44} +(-5.31736 - 0.398481i) q^{45} +(6.80697 + 1.49433i) q^{46} +(-3.14157 + 2.91495i) q^{47} +(9.92276 - 1.07575i) q^{48} +(5.88193 - 3.79511i) q^{49} +(2.99556 + 1.14708i) q^{50} +(3.54565 + 3.82130i) q^{51} +(6.95612 - 10.5757i) q^{52} +(-0.170743 - 0.0127954i) q^{53} +(0.589489 + 0.537933i) q^{54} +(-2.68180 + 3.36287i) q^{55} +(-1.02500 + 7.41278i) q^{56} +(3.58076 + 4.49012i) q^{57} +(0.0881354 - 1.32335i) q^{58} +(-6.28830 + 2.46798i) q^{59} +(4.24215 + 7.07386i) q^{60} +(-0.0851461 + 0.00638082i) q^{61} +(1.53312 - 10.7776i) q^{62} +(-7.11292 + 4.71834i) q^{63} +(-5.29301 - 5.99867i) q^{64} +(10.3441 + 1.55913i) q^{65} +(8.93570 - 2.11767i) q^{66} +(0.684910 + 0.395433i) q^{67} +(0.862026 - 4.08838i) q^{68} +(5.33510 - 11.0785i) q^{69} +(-5.91752 + 1.79684i) q^{70} +(12.8656 - 6.19575i) q^{71} +(1.13499 - 9.05407i) q^{72} +(-7.91929 - 7.34803i) q^{73} +(7.22889 - 3.55544i) q^{74} +(3.18816 - 4.67617i) q^{75} +(1.28365 - 4.42066i) q^{76} +(-0.0874195 + 6.88467i) q^{77} +(-15.3264 - 16.2455i) q^{78} +(5.88861 + 10.1994i) q^{79} +(2.66929 - 6.04849i) q^{80} +(-6.83332 + 4.65888i) q^{81} +(13.0951 + 7.41625i) q^{82} +(-5.33158 - 1.21690i) q^{83} +(12.3095 + 4.77583i) q^{84} +(3.36641 - 0.768360i) q^{85} +(7.32742 + 2.19379i) q^{86} +(-2.23611 - 0.689750i) q^{87} +(-5.51866 - 4.87064i) q^{88} +(1.73014 - 0.533679i) q^{89} +(7.18725 - 2.28246i) q^{90} +(14.6070 - 8.18786i) q^{91} +(-9.71994 + 1.63045i) q^{92} +(-17.8796 - 7.01724i) q^{93} +(2.58426 - 5.48219i) q^{94} +(3.76170 - 0.566986i) q^{95} +(-12.4523 + 6.64653i) q^{96} -0.317284 q^{97} +(-5.71560 + 8.08282i) q^{98} -8.39565i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 648 q - 13 q^{2} - 13 q^{4} - 6 q^{6} - 24 q^{7} - 16 q^{8} - 76 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 648 q - 13 q^{2} - 13 q^{4} - 6 q^{6} - 24 q^{7} - 16 q^{8} - 76 q^{9} - 6 q^{10} - 47 q^{12} - 33 q^{14} - 8 q^{15} - 17 q^{16} - 26 q^{17} - 8 q^{18} - 22 q^{20} - 18 q^{22} - 26 q^{23} - 74 q^{24} - 72 q^{25} - 12 q^{26} + 2 q^{28} - 11 q^{30} + 60 q^{31} - 13 q^{32} - 14 q^{33} - 18 q^{34} + 8 q^{36} - 46 q^{38} - 32 q^{39} + 32 q^{40} - 20 q^{41} - 36 q^{42} + 38 q^{44} - 22 q^{46} - 58 q^{47} + 28 q^{48} - 16 q^{49} - 132 q^{50} + 18 q^{52} - 37 q^{54} - 32 q^{55} + 96 q^{56} - 66 q^{57} + 100 q^{60} + 28 q^{62} - 72 q^{63} - 28 q^{64} - 36 q^{65} - 4 q^{66} - 11 q^{68} - 36 q^{70} + 60 q^{71} - 130 q^{72} - 18 q^{73} - 12 q^{74} + 11 q^{76} - 132 q^{78} - 12 q^{79} - 64 q^{80} - 58 q^{81} + 152 q^{82} - 224 q^{84} + 55 q^{86} - 8 q^{87} - 169 q^{88} - 18 q^{89} + 144 q^{90} - 54 q^{92} + 154 q^{94} - 64 q^{95} - 142 q^{96} - 96 q^{97} + 151 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/392\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(295\) \(297\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{20}{21}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.31212 + 0.527576i −0.927810 + 0.373052i
\(3\) 0.371894 + 2.46736i 0.214713 + 1.42453i 0.793262 + 0.608881i \(0.208381\pi\)
−0.578549 + 0.815648i \(0.696381\pi\)
\(4\) 1.44333 1.38449i 0.721664 0.692244i
\(5\) 1.53857 + 0.603845i 0.688071 + 0.270048i 0.683509 0.729942i \(-0.260453\pi\)
0.00456136 + 0.999990i \(0.498548\pi\)
\(6\) −1.78969 3.04127i −0.730637 1.24159i
\(7\) 2.53791 0.747686i 0.959238 0.282599i
\(8\) −1.16340 + 2.57808i −0.411324 + 0.911489i
\(9\) −3.08282 + 0.950925i −1.02761 + 0.316975i
\(10\) −2.33737 + 0.0193953i −0.739141 + 0.00613334i
\(11\) −0.767062 + 2.48676i −0.231278 + 0.749785i 0.763323 + 0.646017i \(0.223566\pi\)
−0.994601 + 0.103768i \(0.966910\pi\)
\(12\) 3.95279 + 3.04632i 1.14107 + 0.879397i
\(13\) 6.17046 1.40837i 1.71138 0.390610i 0.749051 0.662512i \(-0.230510\pi\)
0.962325 + 0.271902i \(0.0876525\pi\)
\(14\) −2.93558 + 2.31999i −0.784567 + 0.620044i
\(15\) −0.917715 + 4.02077i −0.236953 + 1.03816i
\(16\) 0.166388 3.99654i 0.0415969 0.999134i
\(17\) 1.72613 1.17685i 0.418647 0.285429i −0.335619 0.941998i \(-0.608945\pi\)
0.754266 + 0.656569i \(0.227993\pi\)
\(18\) 3.54335 2.87415i 0.835177 0.677444i
\(19\) 1.99327 1.15081i 0.457287 0.264015i −0.253616 0.967305i \(-0.581620\pi\)
0.710903 + 0.703290i \(0.248286\pi\)
\(20\) 3.05668 1.25859i 0.683495 0.281429i
\(21\) 2.78864 + 5.98386i 0.608531 + 1.30578i
\(22\) −0.305473 3.66761i −0.0651270 0.781937i
\(23\) −4.07160 2.77597i −0.848987 0.578830i 0.0587959 0.998270i \(-0.481274\pi\)
−0.907783 + 0.419441i \(0.862226\pi\)
\(24\) −6.79371 1.91175i −1.38676 0.390234i
\(25\) −1.66268 1.54274i −0.332536 0.308549i
\(26\) −7.35337 + 5.10333i −1.44211 + 1.00085i
\(27\) −0.244841 0.508417i −0.0471196 0.0978449i
\(28\) 2.62787 4.59286i 0.496620 0.867968i
\(29\) −0.406906 + 0.844948i −0.0755605 + 0.156903i −0.935327 0.353784i \(-0.884895\pi\)
0.859767 + 0.510687i \(0.170609\pi\)
\(30\) −0.917109 5.75991i −0.167440 1.05161i
\(31\) −3.84883 + 6.66636i −0.691270 + 1.19731i 0.280153 + 0.959955i \(0.409615\pi\)
−0.971422 + 0.237359i \(0.923718\pi\)
\(32\) 1.89016 + 5.33173i 0.334136 + 0.942525i
\(33\) −6.42098 0.967807i −1.11775 0.168474i
\(34\) −1.64401 + 2.45484i −0.281945 + 0.421001i
\(35\) 4.35624 + 0.382133i 0.736339 + 0.0645922i
\(36\) −3.13298 + 5.64063i −0.522163 + 0.940104i
\(37\) −5.68048 + 0.425693i −0.933864 + 0.0699835i −0.532964 0.846138i \(-0.678922\pi\)
−0.400901 + 0.916122i \(0.631303\pi\)
\(38\) −2.00827 + 2.56161i −0.325784 + 0.415548i
\(39\) 5.76970 + 14.7009i 0.923891 + 2.35404i
\(40\) −3.34674 + 3.26405i −0.529166 + 0.516092i
\(41\) −6.63484 8.31983i −1.03619 1.29934i −0.953054 0.302801i \(-0.902078\pi\)
−0.0831344 0.996538i \(-0.526493\pi\)
\(42\) −6.81597 6.38033i −1.05173 0.984506i
\(43\) −4.22854 3.37215i −0.644846 0.514247i 0.245580 0.969376i \(-0.421022\pi\)
−0.890426 + 0.455129i \(0.849593\pi\)
\(44\) 2.33576 + 4.65119i 0.352129 + 0.701193i
\(45\) −5.31736 0.398481i −0.792665 0.0594020i
\(46\) 6.80697 + 1.49433i 1.00363 + 0.220327i
\(47\) −3.14157 + 2.91495i −0.458245 + 0.425189i −0.875217 0.483730i \(-0.839282\pi\)
0.416972 + 0.908919i \(0.363091\pi\)
\(48\) 9.92276 1.07575i 1.43223 0.155271i
\(49\) 5.88193 3.79511i 0.840276 0.542159i
\(50\) 2.99556 + 1.14708i 0.423636 + 0.162221i
\(51\) 3.54565 + 3.82130i 0.496490 + 0.535089i
\(52\) 6.95612 10.5757i 0.964640 1.46658i
\(53\) −0.170743 0.0127954i −0.0234534 0.00175759i 0.0629982 0.998014i \(-0.479934\pi\)
−0.0864516 + 0.996256i \(0.527553\pi\)
\(54\) 0.589489 + 0.537933i 0.0802193 + 0.0732034i
\(55\) −2.68180 + 3.36287i −0.361613 + 0.453449i
\(56\) −1.02500 + 7.41278i −0.136972 + 0.990575i
\(57\) 3.58076 + 4.49012i 0.474283 + 0.594732i
\(58\) 0.0881354 1.32335i 0.0115727 0.173764i
\(59\) −6.28830 + 2.46798i −0.818667 + 0.321303i −0.737457 0.675394i \(-0.763974\pi\)
−0.0812099 + 0.996697i \(0.525878\pi\)
\(60\) 4.24215 + 7.07386i 0.547659 + 0.913231i
\(61\) −0.0851461 + 0.00638082i −0.0109018 + 0.000816980i −0.0801799 0.996780i \(-0.525549\pi\)
0.0692781 + 0.997597i \(0.477930\pi\)
\(62\) 1.53312 10.7776i 0.194706 1.36876i
\(63\) −7.11292 + 4.71834i −0.896144 + 0.594455i
\(64\) −5.29301 5.99867i −0.661626 0.749834i
\(65\) 10.3441 + 1.55913i 1.28303 + 0.193386i
\(66\) 8.93570 2.11767i 1.09991 0.260668i
\(67\) 0.684910 + 0.395433i 0.0836751 + 0.0483099i 0.541254 0.840859i \(-0.317950\pi\)
−0.457579 + 0.889169i \(0.651283\pi\)
\(68\) 0.862026 4.08838i 0.104536 0.495789i
\(69\) 5.33510 11.0785i 0.642271 1.33369i
\(70\) −5.91752 + 1.79684i −0.707279 + 0.214764i
\(71\) 12.8656 6.19575i 1.52687 0.735300i 0.533023 0.846101i \(-0.321056\pi\)
0.993843 + 0.110801i \(0.0353417\pi\)
\(72\) 1.13499 9.05407i 0.133760 1.06703i
\(73\) −7.91929 7.34803i −0.926883 0.860022i 0.0635553 0.997978i \(-0.479756\pi\)
−0.990438 + 0.137957i \(0.955947\pi\)
\(74\) 7.22889 3.55544i 0.840341 0.413312i
\(75\) 3.18816 4.67617i 0.368137 0.539957i
\(76\) 1.28365 4.42066i 0.147245 0.507084i
\(77\) −0.0874195 + 6.88467i −0.00996238 + 0.784581i
\(78\) −15.3264 16.2455i −1.73537 1.83944i
\(79\) 5.88861 + 10.1994i 0.662521 + 1.14752i 0.979951 + 0.199238i \(0.0638466\pi\)
−0.317431 + 0.948281i \(0.602820\pi\)
\(80\) 2.66929 6.04849i 0.298436 0.676242i
\(81\) −6.83332 + 4.65888i −0.759258 + 0.517654i
\(82\) 13.0951 + 7.41625i 1.44611 + 0.818987i
\(83\) −5.33158 1.21690i −0.585217 0.133572i −0.0803465 0.996767i \(-0.525603\pi\)
−0.504871 + 0.863195i \(0.668460\pi\)
\(84\) 12.3095 + 4.77583i 1.34308 + 0.521085i
\(85\) 3.36641 0.768360i 0.365138 0.0833404i
\(86\) 7.32742 + 2.19379i 0.790136 + 0.236563i
\(87\) −2.23611 0.689750i −0.239737 0.0739489i
\(88\) −5.51866 4.87064i −0.588291 0.519212i
\(89\) 1.73014 0.533679i 0.183395 0.0565698i −0.201698 0.979448i \(-0.564646\pi\)
0.385092 + 0.922878i \(0.374170\pi\)
\(90\) 7.18725 2.28246i 0.757603 0.240592i
\(91\) 14.6070 8.18786i 1.53123 0.858321i
\(92\) −9.71994 + 1.63045i −1.01337 + 0.169986i
\(93\) −17.8796 7.01724i −1.85403 0.727654i
\(94\) 2.58426 5.48219i 0.266546 0.565444i
\(95\) 3.76170 0.566986i 0.385943 0.0581715i
\(96\) −12.4523 + 6.64653i −1.27091 + 0.678358i
\(97\) −0.317284 −0.0322154 −0.0161077 0.999870i \(-0.505127\pi\)
−0.0161077 + 0.999870i \(0.505127\pi\)
\(98\) −5.71560 + 8.08282i −0.577363 + 0.816488i
\(99\) 8.39565i 0.843794i
\(100\) −4.53570 + 0.0752790i −0.453570 + 0.00752790i
\(101\) 2.44347 + 16.2113i 0.243134 + 1.61309i 0.693644 + 0.720318i \(0.256004\pi\)
−0.450510 + 0.892771i \(0.648758\pi\)
\(102\) −6.66835 3.14341i −0.660265 0.311244i
\(103\) 6.65813 16.9646i 0.656045 1.67158i −0.0818371 0.996646i \(-0.526079\pi\)
0.737882 0.674930i \(-0.235826\pi\)
\(104\) −3.54782 + 17.5464i −0.347892 + 1.72057i
\(105\) 0.677202 + 10.8905i 0.0660881 + 1.06280i
\(106\) 0.230786 0.0732908i 0.0224160 0.00711863i
\(107\) 3.63296 + 11.7778i 0.351212 + 1.13860i 0.943080 + 0.332566i \(0.107914\pi\)
−0.591868 + 0.806035i \(0.701609\pi\)
\(108\) −1.05728 0.394833i −0.101737 0.0379928i
\(109\) 4.08949 13.2578i 0.391702 1.26987i −0.518276 0.855213i \(-0.673426\pi\)
0.909979 0.414655i \(-0.136098\pi\)
\(110\) 1.74468 5.82734i 0.166348 0.555615i
\(111\) −3.16287 13.8574i −0.300206 1.31529i
\(112\) −2.56588 10.2672i −0.242453 0.970163i
\(113\) 3.68853 16.1605i 0.346988 1.52025i −0.436991 0.899466i \(-0.643956\pi\)
0.783979 0.620787i \(-0.213187\pi\)
\(114\) −7.06727 4.00247i −0.661910 0.374866i
\(115\) −4.58820 6.72965i −0.427851 0.627543i
\(116\) 0.582522 + 1.78289i 0.0540858 + 0.165537i
\(117\) −17.6832 + 10.2094i −1.63481 + 0.943858i
\(118\) 6.94897 6.55584i 0.639705 0.603514i
\(119\) 3.50083 4.27734i 0.320920 0.392103i
\(120\) −9.29821 7.04371i −0.848807 0.643000i
\(121\) 3.49306 + 2.38153i 0.317551 + 0.216502i
\(122\) 0.108356 0.0532935i 0.00981007 0.00482496i
\(123\) 18.0605 19.4646i 1.62846 1.75507i
\(124\) 3.67438 + 14.9504i 0.329969 + 1.34259i
\(125\) −5.21225 10.8234i −0.466198 0.968070i
\(126\) 6.84373 9.94365i 0.609688 0.885850i
\(127\) −6.55145 3.15501i −0.581347 0.279962i 0.120009 0.992773i \(-0.461708\pi\)
−0.701356 + 0.712811i \(0.747422\pi\)
\(128\) 10.1098 + 5.07853i 0.893591 + 0.448883i
\(129\) 6.74772 11.6874i 0.594103 1.02902i
\(130\) −14.3953 + 3.41155i −1.26255 + 0.299213i
\(131\) 1.64027 10.8825i 0.143311 0.950808i −0.795395 0.606091i \(-0.792737\pi\)
0.938707 0.344717i \(-0.112025\pi\)
\(132\) −10.6075 + 7.49290i −0.923263 + 0.652173i
\(133\) 4.19828 4.41100i 0.364037 0.382482i
\(134\) −1.10731 0.157514i −0.0956567 0.0136072i
\(135\) −0.0697000 0.930082i −0.00599882 0.0800487i
\(136\) 1.02585 + 5.81924i 0.0879658 + 0.498996i
\(137\) 2.25712 + 5.75104i 0.192838 + 0.491344i 0.994290 0.106716i \(-0.0340335\pi\)
−0.801451 + 0.598060i \(0.795938\pi\)
\(138\) −1.15558 + 17.3509i −0.0983694 + 1.47701i
\(139\) −3.00358 + 2.39528i −0.254760 + 0.203165i −0.742539 0.669803i \(-0.766379\pi\)
0.487779 + 0.872967i \(0.337807\pi\)
\(140\) 6.81654 5.47962i 0.576103 0.463112i
\(141\) −8.36055 6.66732i −0.704085 0.561489i
\(142\) −13.6125 + 14.9172i −1.14234 + 1.25182i
\(143\) −1.23086 + 16.4247i −0.102930 + 1.37350i
\(144\) 3.28746 + 12.4788i 0.273955 + 1.03990i
\(145\) −1.13627 + 1.05431i −0.0943622 + 0.0875554i
\(146\) 14.2677 + 5.46348i 1.18080 + 0.452161i
\(147\) 11.5514 + 13.1014i 0.952740 + 1.08059i
\(148\) −7.60942 + 8.47896i −0.625490 + 0.696966i
\(149\) 9.33339 + 10.0590i 0.764621 + 0.824065i 0.988606 0.150527i \(-0.0480971\pi\)
−0.223985 + 0.974593i \(0.571907\pi\)
\(150\) −1.71622 + 7.81769i −0.140128 + 0.638312i
\(151\) 0.219759 2.93248i 0.0178837 0.238641i −0.981098 0.193514i \(-0.938012\pi\)
0.998981 0.0451275i \(-0.0143694\pi\)
\(152\) 0.647926 + 6.47767i 0.0525538 + 0.525408i
\(153\) −4.20224 + 5.26944i −0.339731 + 0.426009i
\(154\) −3.51748 9.07965i −0.283447 0.731659i
\(155\) −9.94715 + 7.93259i −0.798974 + 0.637161i
\(156\) 28.6808 + 13.2302i 2.29631 + 1.05926i
\(157\) −10.2718 + 4.03139i −0.819780 + 0.321740i −0.737907 0.674903i \(-0.764186\pi\)
−0.0818733 + 0.996643i \(0.526090\pi\)
\(158\) −13.1075 10.2761i −1.04278 0.817525i
\(159\) −0.0319275 0.426043i −0.00253202 0.0337874i
\(160\) −0.311395 + 9.34461i −0.0246179 + 0.738756i
\(161\) −12.4089 4.00087i −0.977957 0.315313i
\(162\) 6.50824 9.71812i 0.511336 0.763527i
\(163\) −3.45458 + 22.9196i −0.270583 + 1.79520i 0.279555 + 0.960130i \(0.409813\pi\)
−0.550139 + 0.835073i \(0.685425\pi\)
\(164\) −21.0950 2.82238i −1.64724 0.220391i
\(165\) −9.29474 5.36632i −0.723594 0.417767i
\(166\) 7.63769 1.21609i 0.592800 0.0943873i
\(167\) 7.90811 + 3.80834i 0.611948 + 0.294699i 0.714071 0.700073i \(-0.246849\pi\)
−0.102123 + 0.994772i \(0.532564\pi\)
\(168\) −18.6712 + 0.227728i −1.44051 + 0.0175696i
\(169\) 24.3784 11.7400i 1.87526 0.903079i
\(170\) −4.01177 + 2.78422i −0.307689 + 0.213540i
\(171\) −5.05056 + 5.44321i −0.386226 + 0.416253i
\(172\) −10.7719 + 0.987247i −0.821346 + 0.0752769i
\(173\) −5.99839 + 8.79802i −0.456049 + 0.668901i −0.983546 0.180655i \(-0.942178\pi\)
0.527497 + 0.849557i \(0.323130\pi\)
\(174\) 3.29795 0.274684i 0.250017 0.0208237i
\(175\) −5.37322 2.67217i −0.406177 0.201997i
\(176\) 9.81078 + 3.47936i 0.739516 + 0.262267i
\(177\) −8.42796 14.5977i −0.633484 1.09723i
\(178\) −1.98860 + 1.61303i −0.149052 + 0.120902i
\(179\) 1.48679 + 2.18072i 0.111128 + 0.162995i 0.877774 0.479076i \(-0.159028\pi\)
−0.766646 + 0.642070i \(0.778076\pi\)
\(180\) −8.22638 + 6.78668i −0.613158 + 0.505849i
\(181\) 14.9702 + 3.41685i 1.11272 + 0.253972i 0.739092 0.673605i \(-0.235255\pi\)
0.373633 + 0.927577i \(0.378112\pi\)
\(182\) −14.8465 + 18.4498i −1.10049 + 1.36759i
\(183\) −0.0474091 0.207713i −0.00350458 0.0153546i
\(184\) 11.8936 7.26735i 0.876805 0.535756i
\(185\) −8.99688 2.77517i −0.661464 0.204035i
\(186\) 27.1624 0.225391i 1.99164 0.0165265i
\(187\) 1.60250 + 5.19517i 0.117186 + 0.379909i
\(188\) −0.498600 + 8.55669i −0.0363641 + 0.624061i
\(189\) −1.00152 1.10725i −0.0728498 0.0805406i
\(190\) −4.63669 + 2.72854i −0.336381 + 0.197949i
\(191\) 2.93325 7.47380i 0.212243 0.540785i −0.784616 0.619981i \(-0.787140\pi\)
0.996859 + 0.0791962i \(0.0252354\pi\)
\(192\) 12.8324 15.2906i 0.926101 1.10350i
\(193\) −1.05325 + 0.158751i −0.0758143 + 0.0114272i −0.186840 0.982390i \(-0.559825\pi\)
0.111026 + 0.993818i \(0.464586\pi\)
\(194\) 0.416316 0.167392i 0.0298897 0.0120180i
\(195\) 26.1025i 1.86924i
\(196\) 3.23526 13.6211i 0.231090 0.972932i
\(197\) 9.73650i 0.693697i −0.937921 0.346848i \(-0.887252\pi\)
0.937921 0.346848i \(-0.112748\pi\)
\(198\) 4.42934 + 11.0161i 0.314780 + 0.782881i
\(199\) −7.19911 + 1.08509i −0.510331 + 0.0769201i −0.399160 0.916881i \(-0.630698\pi\)
−0.111171 + 0.993801i \(0.535460\pi\)
\(200\) 5.91168 2.49170i 0.418019 0.176190i
\(201\) −0.720960 + 1.83698i −0.0508526 + 0.129570i
\(202\) −11.7588 19.9821i −0.827349 1.40594i
\(203\) −0.400932 + 2.44864i −0.0281399 + 0.171861i
\(204\) 10.4081 + 0.606481i 0.728711 + 0.0424621i
\(205\) −5.18430 16.8071i −0.362087 1.17386i
\(206\) 0.213857 + 25.7723i 0.0149001 + 1.79564i
\(207\) 15.1918 + 4.68604i 1.05590 + 0.325702i
\(208\) −4.60190 24.8948i −0.319084 1.72614i
\(209\) 1.33283 + 5.83952i 0.0921940 + 0.403928i
\(210\) −6.63414 13.9324i −0.457799 0.961427i
\(211\) −17.1798 3.92118i −1.18271 0.269945i −0.414442 0.910076i \(-0.636023\pi\)
−0.768266 + 0.640130i \(0.778880\pi\)
\(212\) −0.264153 + 0.217924i −0.0181421 + 0.0149671i
\(213\) 20.0717 + 29.4399i 1.37529 + 2.01719i
\(214\) −10.9806 13.5372i −0.750616 0.925385i
\(215\) −4.46966 7.74167i −0.304828 0.527978i
\(216\) 1.59559 0.0397275i 0.108566 0.00270311i
\(217\) −4.78361 + 19.7963i −0.324733 + 1.34386i
\(218\) 1.62859 + 19.5534i 0.110302 + 1.32432i
\(219\) 15.1851 22.2724i 1.02611 1.50503i
\(220\) 0.785137 + 8.56663i 0.0529339 + 0.577562i
\(221\) 8.99354 9.69273i 0.604971 0.652004i
\(222\) 11.4609 + 16.5140i 0.769207 + 1.10835i
\(223\) 14.9706 7.20944i 1.00250 0.482780i 0.140716 0.990050i \(-0.455060\pi\)
0.861787 + 0.507270i \(0.169345\pi\)
\(224\) 8.78350 + 12.1182i 0.586872 + 0.809680i
\(225\) 6.59279 + 3.17492i 0.439519 + 0.211661i
\(226\) 3.68609 + 23.1505i 0.245195 + 1.53995i
\(227\) −20.3905 11.7725i −1.35336 0.781365i −0.364645 0.931146i \(-0.618810\pi\)
−0.988719 + 0.149781i \(0.952143\pi\)
\(228\) 11.3847 + 1.52321i 0.753972 + 0.100877i
\(229\) 0.00666470 0.0442174i 0.000440416 0.00292197i −0.988610 0.150503i \(-0.951911\pi\)
0.989050 + 0.147581i \(0.0471487\pi\)
\(230\) 9.57067 + 6.40949i 0.631071 + 0.422630i
\(231\) −17.0195 + 2.34467i −1.11980 + 0.154268i
\(232\) −1.70495 2.03205i −0.111936 0.133410i
\(233\) −1.70931 22.8091i −0.111981 1.49428i −0.716445 0.697644i \(-0.754232\pi\)
0.604464 0.796632i \(-0.293387\pi\)
\(234\) 17.8163 22.7252i 1.16468 1.48559i
\(235\) −6.59371 + 2.58784i −0.430126 + 0.168812i
\(236\) −5.65919 + 12.2682i −0.368382 + 0.798590i
\(237\) −22.9755 + 18.3224i −1.49242 + 1.19017i
\(238\) −2.33689 + 7.45934i −0.151478 + 0.483518i
\(239\) −9.67470 + 12.1317i −0.625804 + 0.784734i −0.989148 0.146921i \(-0.953064\pi\)
0.363344 + 0.931655i \(0.381635\pi\)
\(240\) 15.9165 + 4.33669i 1.02740 + 0.279932i
\(241\) −2.18264 + 29.1253i −0.140596 + 1.87613i 0.268010 + 0.963416i \(0.413634\pi\)
−0.408607 + 0.912711i \(0.633985\pi\)
\(242\) −5.83975 1.28200i −0.375394 0.0824101i
\(243\) −15.1879 16.3686i −0.974302 1.05005i
\(244\) −0.114060 + 0.127093i −0.00730192 + 0.00813632i
\(245\) 11.3414 2.28728i 0.724578 0.146129i
\(246\) −13.4285 + 35.0682i −0.856173 + 2.23587i
\(247\) 10.6786 9.90830i 0.679464 0.630450i
\(248\) −12.7087 17.6782i −0.807003 1.12257i
\(249\) 1.01974 13.6075i 0.0646233 0.862338i
\(250\) 12.5492 + 11.4517i 0.793684 + 0.724269i
\(251\) −9.29460 7.41220i −0.586670 0.467854i 0.284608 0.958644i \(-0.408137\pi\)
−0.871278 + 0.490790i \(0.836708\pi\)
\(252\) −3.73379 + 16.6579i −0.235206 + 1.04935i
\(253\) 10.0263 7.99573i 0.630350 0.502687i
\(254\) 10.2608 + 0.683373i 0.643820 + 0.0428786i
\(255\) 3.14777 + 8.02038i 0.197121 + 0.502255i
\(256\) −15.9446 1.32995i −0.996539 0.0831218i
\(257\) −1.31227 17.5110i −0.0818570 1.09231i −0.875274 0.483627i \(-0.839319\pi\)
0.793417 0.608678i \(-0.208300\pi\)
\(258\) −2.68784 + 18.8952i −0.167338 + 1.17636i
\(259\) −14.0982 + 5.32758i −0.876021 + 0.331040i
\(260\) 17.0886 12.0710i 1.05979 0.748611i
\(261\) 0.450936 2.99176i 0.0279122 0.185185i
\(262\) 3.58911 + 15.1445i 0.221736 + 0.935632i
\(263\) −2.13459 + 3.69722i −0.131625 + 0.227980i −0.924303 0.381660i \(-0.875353\pi\)
0.792678 + 0.609640i \(0.208686\pi\)
\(264\) 9.96524 15.4279i 0.613318 0.949519i
\(265\) −0.254974 0.122789i −0.0156630 0.00754288i
\(266\) −3.18152 + 8.00268i −0.195072 + 0.490676i
\(267\) 1.96021 + 4.07041i 0.119963 + 0.249105i
\(268\) 1.53602 0.377510i 0.0938275 0.0230601i
\(269\) 13.8478 14.9243i 0.844314 0.909954i −0.152614 0.988286i \(-0.548769\pi\)
0.996927 + 0.0783323i \(0.0249595\pi\)
\(270\) 0.582144 + 1.18361i 0.0354282 + 0.0720322i
\(271\) 2.69831 + 1.83968i 0.163911 + 0.111752i 0.642497 0.766288i \(-0.277898\pi\)
−0.478587 + 0.878040i \(0.658851\pi\)
\(272\) −4.41613 7.09434i −0.267767 0.430158i
\(273\) 25.6346 + 32.9957i 1.55148 + 1.99699i
\(274\) −5.99572 6.35526i −0.362215 0.383935i
\(275\) 5.11181 2.95130i 0.308254 0.177970i
\(276\) −7.63768 23.3762i −0.459734 1.40708i
\(277\) 1.97215 + 2.89261i 0.118495 + 0.173800i 0.880904 0.473296i \(-0.156936\pi\)
−0.762409 + 0.647096i \(0.775983\pi\)
\(278\) 2.67737 4.72751i 0.160578 0.283537i
\(279\) 5.52604 24.2112i 0.330835 1.44948i
\(280\) −6.05321 + 10.7862i −0.361749 + 0.644597i
\(281\) 4.27294 + 18.7210i 0.254902 + 1.11680i 0.926622 + 0.375994i \(0.122699\pi\)
−0.671720 + 0.740805i \(0.734444\pi\)
\(282\) 14.4876 + 4.33751i 0.862723 + 0.258295i
\(283\) 4.54683 14.7404i 0.270281 0.876229i −0.714080 0.700064i \(-0.753155\pi\)
0.984361 0.176165i \(-0.0563691\pi\)
\(284\) 9.99134 26.7547i 0.592877 1.58760i
\(285\) 2.79791 + 9.07061i 0.165734 + 0.537296i
\(286\) −7.05024 22.2006i −0.416890 1.31275i
\(287\) −23.0592 16.1542i −1.36114 0.953550i
\(288\) −10.8971 14.6394i −0.642117 0.862633i
\(289\) −4.61627 + 11.7621i −0.271545 + 0.691886i
\(290\) 0.934701 1.98285i 0.0548875 0.116437i
\(291\) −0.117996 0.782854i −0.00691706 0.0458917i
\(292\) −21.6034 + 0.358551i −1.26424 + 0.0209826i
\(293\) 2.20743i 0.128960i 0.997919 + 0.0644798i \(0.0205388\pi\)
−0.997919 + 0.0644798i \(0.979461\pi\)
\(294\) −22.0688 11.0965i −1.28708 0.647159i
\(295\) −11.1653 −0.650068
\(296\) 5.51119 15.1400i 0.320331 0.879993i
\(297\) 1.45212 0.218871i 0.0842604 0.0127002i
\(298\) −17.5534 8.27456i −1.01684 0.479332i
\(299\) −29.0332 11.3947i −1.67903 0.658972i
\(300\) −1.87254 11.1632i −0.108111 0.644508i
\(301\) −13.2529 5.39657i −0.763886 0.311053i
\(302\) 1.25875 + 3.96370i 0.0724331 + 0.228086i
\(303\) −39.0905 + 12.0578i −2.24569 + 0.692703i
\(304\) −4.26762 8.15766i −0.244765 0.467874i
\(305\) −0.134857 0.0415977i −0.00772186 0.00238188i
\(306\) 2.73382 9.13115i 0.156282 0.521993i
\(307\) −21.5147 + 4.91059i −1.22791 + 0.280262i −0.786809 0.617197i \(-0.788268\pi\)
−0.441099 + 0.897459i \(0.645411\pi\)
\(308\) 9.40557 + 10.0579i 0.535932 + 0.573100i
\(309\) 44.3339 + 10.1189i 2.52207 + 0.575646i
\(310\) 8.86683 15.6564i 0.503602 0.889224i
\(311\) −10.2193 + 6.96738i −0.579482 + 0.395084i −0.817289 0.576228i \(-0.804524\pi\)
0.237807 + 0.971312i \(0.423571\pi\)
\(312\) −44.6127 2.22832i −2.52570 0.126154i
\(313\) −3.30837 5.73026i −0.187000 0.323894i 0.757249 0.653127i \(-0.226543\pi\)
−0.944249 + 0.329233i \(0.893210\pi\)
\(314\) 11.3510 10.7088i 0.640574 0.604335i
\(315\) −13.7929 + 2.96441i −0.777142 + 0.167026i
\(316\) 22.6201 + 6.56833i 1.27248 + 0.369497i
\(317\) 4.08703 5.99457i 0.229550 0.336688i −0.694132 0.719848i \(-0.744212\pi\)
0.923682 + 0.383159i \(0.125164\pi\)
\(318\) 0.266663 + 0.542176i 0.0149537 + 0.0304037i
\(319\) −1.78906 1.66000i −0.100168 0.0929423i
\(320\) −4.52140 12.4256i −0.252754 0.694610i
\(321\) −27.7089 + 13.3439i −1.54656 + 0.744784i
\(322\) 18.3927 1.29700i 1.02499 0.0722791i
\(323\) 2.08629 4.33224i 0.116085 0.241052i
\(324\) −3.41256 + 16.1849i −0.189587 + 0.899164i
\(325\) −12.4323 7.17776i −0.689617 0.398151i
\(326\) −7.55901 31.8959i −0.418655 1.76655i
\(327\) 34.2326 + 5.15973i 1.89307 + 0.285334i
\(328\) 29.1682 7.42588i 1.61054 0.410026i
\(329\) −5.79354 + 9.74678i −0.319408 + 0.537357i
\(330\) 15.0270 + 2.13758i 0.827207 + 0.117670i
\(331\) −14.0945 + 1.05624i −0.774705 + 0.0580561i −0.456214 0.889870i \(-0.650795\pi\)
−0.318490 + 0.947926i \(0.603176\pi\)
\(332\) −9.38000 + 5.62513i −0.514794 + 0.308719i
\(333\) 17.1071 6.71404i 0.937463 0.367927i
\(334\) −12.3856 0.824884i −0.677709 0.0451357i
\(335\) 0.815004 + 1.02198i 0.0445284 + 0.0558369i
\(336\) 24.3787 10.1493i 1.32997 0.553688i
\(337\) −7.40089 + 9.28042i −0.403152 + 0.505537i −0.941420 0.337237i \(-0.890508\pi\)
0.538268 + 0.842774i \(0.319079\pi\)
\(338\) −25.7937 + 28.2658i −1.40299 + 1.53746i
\(339\) 41.2455 + 3.09092i 2.24015 + 0.167876i
\(340\) 3.79504 5.76974i 0.205815 0.312908i
\(341\) −13.6253 14.6846i −0.737853 0.795216i
\(342\) 3.75524 9.80671i 0.203060 0.530286i
\(343\) 12.0902 14.0295i 0.652811 0.757521i
\(344\) 13.6131 6.97836i 0.733971 0.376248i
\(345\) 14.8981 13.8234i 0.802087 0.744228i
\(346\) 3.22899 14.7087i 0.173592 0.790744i
\(347\) 26.4301 + 1.98067i 1.41884 + 0.106328i 0.761941 0.647647i \(-0.224247\pi\)
0.656904 + 0.753974i \(0.271866\pi\)
\(348\) −4.18239 + 2.10034i −0.224200 + 0.112590i
\(349\) 23.2353 + 18.5295i 1.24376 + 0.991863i 0.999756 + 0.0220878i \(0.00703133\pi\)
0.244001 + 0.969775i \(0.421540\pi\)
\(350\) 8.46009 + 0.671436i 0.452211 + 0.0358898i
\(351\) −2.22682 2.79234i −0.118859 0.149044i
\(352\) −14.7086 + 0.610589i −0.783969 + 0.0325445i
\(353\) −9.35869 23.8456i −0.498113 1.26917i −0.930105 0.367294i \(-0.880284\pi\)
0.431992 0.901877i \(-0.357811\pi\)
\(354\) 18.7599 + 14.7075i 0.997076 + 0.781695i
\(355\) 23.5359 1.76377i 1.24916 0.0936114i
\(356\) 1.75829 3.16564i 0.0931893 0.167778i
\(357\) 11.8557 + 7.04707i 0.627468 + 0.372971i
\(358\) −3.10135 2.07698i −0.163911 0.109772i
\(359\) −10.4304 1.57213i −0.550497 0.0829740i −0.132097 0.991237i \(-0.542171\pi\)
−0.418400 + 0.908263i \(0.637409\pi\)
\(360\) 7.21353 13.2450i 0.380186 0.698072i
\(361\) −6.85125 + 11.8667i −0.360592 + 0.624564i
\(362\) −21.4453 + 3.41459i −1.12714 + 0.179467i
\(363\) −4.57703 + 9.50430i −0.240232 + 0.498846i
\(364\) 9.74671 32.0410i 0.510866 1.67941i
\(365\) −7.74733 16.0875i −0.405514 0.842058i
\(366\) 0.171791 + 0.247533i 0.00897965 + 0.0129387i
\(367\) −11.0640 10.2659i −0.577536 0.535875i 0.336408 0.941716i \(-0.390788\pi\)
−0.913943 + 0.405841i \(0.866979\pi\)
\(368\) −11.7717 + 15.8104i −0.613644 + 0.824175i
\(369\) 28.3656 + 19.3393i 1.47665 + 1.00677i
\(370\) 13.2691 1.10518i 0.689828 0.0574554i
\(371\) −0.442897 + 0.0951887i −0.0229941 + 0.00494195i
\(372\) −35.5215 + 14.6260i −1.84170 + 0.758321i
\(373\) 9.54196 5.50905i 0.494064 0.285248i −0.232195 0.972669i \(-0.574591\pi\)
0.726259 + 0.687421i \(0.241257\pi\)
\(374\) −4.84352 5.97126i −0.250452 0.308766i
\(375\) 24.7667 16.8856i 1.27894 0.871970i
\(376\) −3.86008 11.4905i −0.199068 0.592576i
\(377\) −1.32080 + 5.78679i −0.0680245 + 0.298035i
\(378\) 1.89827 + 0.924470i 0.0976366 + 0.0475496i
\(379\) 20.9952 4.79203i 1.07845 0.246150i 0.353840 0.935306i \(-0.384876\pi\)
0.724613 + 0.689156i \(0.242019\pi\)
\(380\) 4.64439 6.02638i 0.238252 0.309147i
\(381\) 5.34809 17.3381i 0.273991 0.888257i
\(382\) 0.0942150 + 11.3540i 0.00482046 + 0.580924i
\(383\) 30.1153 9.28934i 1.53882 0.474663i 0.594612 0.804013i \(-0.297306\pi\)
0.944208 + 0.329350i \(0.106830\pi\)
\(384\) −8.77075 + 26.8332i −0.447581 + 1.36933i
\(385\) −4.29178 + 10.5398i −0.218729 + 0.537157i
\(386\) 1.29823 0.763968i 0.0660783 0.0388849i
\(387\) 16.2425 + 6.37471i 0.825652 + 0.324045i
\(388\) −0.457945 + 0.439276i −0.0232487 + 0.0223009i
\(389\) 1.61923 + 10.7429i 0.0820981 + 0.544685i 0.991636 + 0.129065i \(0.0411974\pi\)
−0.909538 + 0.415620i \(0.863564\pi\)
\(390\) −13.7710 34.2496i −0.697324 1.73430i
\(391\) −10.2950 −0.520640
\(392\) 2.94108 + 19.5793i 0.148547 + 0.988905i
\(393\) 27.4610 1.38522
\(394\) 5.13674 + 12.7755i 0.258785 + 0.643619i
\(395\) 2.90121 + 19.2483i 0.145976 + 0.968487i
\(396\) −11.6237 12.1177i −0.584111 0.608936i
\(397\) 24.6612 + 9.67879i 1.23771 + 0.485765i 0.891768 0.452492i \(-0.149465\pi\)
0.345940 + 0.938257i \(0.387560\pi\)
\(398\) 8.87364 5.22185i 0.444795 0.261748i
\(399\) 12.4448 + 8.71823i 0.623020 + 0.436458i
\(400\) −6.44228 + 6.38828i −0.322114 + 0.319414i
\(401\) −9.95426 + 3.07048i −0.497092 + 0.153333i −0.533156 0.846017i \(-0.678994\pi\)
0.0360640 + 0.999349i \(0.488518\pi\)
\(402\) −0.0231570 2.79070i −0.00115497 0.139187i
\(403\) −14.3603 + 46.5550i −0.715339 + 2.31907i
\(404\) 25.9711 + 20.0153i 1.29211 + 0.995800i
\(405\) −13.3268 + 3.04176i −0.662215 + 0.151146i
\(406\) −0.765770 3.42443i −0.0380045 0.169952i
\(407\) 3.29869 14.4525i 0.163510 0.716383i
\(408\) −13.9766 + 4.69528i −0.691946 + 0.232451i
\(409\) 22.9421 15.6417i 1.13442 0.773432i 0.157598 0.987503i \(-0.449625\pi\)
0.976818 + 0.214072i \(0.0686726\pi\)
\(410\) 15.6694 + 19.3178i 0.773859 + 0.954040i
\(411\) −13.3505 + 7.70789i −0.658529 + 0.380202i
\(412\) −13.8775 33.7036i −0.683694 1.66046i
\(413\) −14.1138 + 10.9652i −0.694497 + 0.539561i
\(414\) −22.4057 + 1.86615i −1.10118 + 0.0917165i
\(415\) −7.46821 5.09174i −0.366600 0.249944i
\(416\) 19.1721 + 30.2371i 0.939992 + 1.48250i
\(417\) −7.02701 6.52011i −0.344114 0.319291i
\(418\) −4.82963 6.95899i −0.236225 0.340375i
\(419\) −11.1333 23.1186i −0.543900 1.12942i −0.973981 0.226629i \(-0.927229\pi\)
0.430081 0.902790i \(-0.358485\pi\)
\(420\) 16.0552 + 14.7810i 0.783414 + 0.721238i
\(421\) −4.97902 + 10.3390i −0.242663 + 0.503894i −0.986356 0.164627i \(-0.947358\pi\)
0.743693 + 0.668521i \(0.233072\pi\)
\(422\) 24.6107 3.91859i 1.19803 0.190754i
\(423\) 6.91300 11.9737i 0.336122 0.582180i
\(424\) 0.231630 0.425304i 0.0112490 0.0206546i
\(425\) −4.68558 0.706237i −0.227284 0.0342575i
\(426\) −41.8683 28.0393i −2.02853 1.35851i
\(427\) −0.211322 + 0.0798565i −0.0102266 + 0.00386453i
\(428\) 21.5497 + 11.9694i 1.04165 + 0.578563i
\(429\) −40.9834 + 3.07128i −1.97870 + 0.148283i
\(430\) 9.94906 + 7.79994i 0.479786 + 0.376146i
\(431\) 8.80260 + 22.4287i 0.424006 + 1.08035i 0.970117 + 0.242638i \(0.0780126\pi\)
−0.546111 + 0.837713i \(0.683892\pi\)
\(432\) −2.07265 + 0.893921i −0.0997202 + 0.0430088i
\(433\) 24.1197 + 30.2451i 1.15912 + 1.45349i 0.867836 + 0.496851i \(0.165510\pi\)
0.291282 + 0.956637i \(0.405918\pi\)
\(434\) −4.16738 28.4989i −0.200041 1.36799i
\(435\) −3.02392 2.41150i −0.144986 0.115622i
\(436\) −12.4528 24.7972i −0.596381 1.18757i
\(437\) −11.3104 0.847599i −0.541051 0.0405461i
\(438\) −8.17427 + 37.2354i −0.390582 + 1.77918i
\(439\) −12.0382 + 11.1698i −0.574552 + 0.533106i −0.913043 0.407863i \(-0.866274\pi\)
0.338491 + 0.940970i \(0.390083\pi\)
\(440\) −5.54975 10.8262i −0.264574 0.516121i
\(441\) −14.5241 + 17.2929i −0.691623 + 0.823473i
\(442\) −6.68697 + 17.4628i −0.318067 + 0.830622i
\(443\) −10.6429 11.4703i −0.505659 0.544971i 0.427697 0.903922i \(-0.359325\pi\)
−0.933356 + 0.358951i \(0.883135\pi\)
\(444\) −23.7505 15.6219i −1.12715 0.741381i
\(445\) 2.98421 + 0.223636i 0.141465 + 0.0106013i
\(446\) −15.8397 + 17.3578i −0.750030 + 0.821915i
\(447\) −21.3481 + 26.7697i −1.00973 + 1.26616i
\(448\) −17.9183 11.2666i −0.846559 0.532295i
\(449\) 2.17021 + 2.72136i 0.102419 + 0.128429i 0.830399 0.557169i \(-0.188112\pi\)
−0.727981 + 0.685598i \(0.759541\pi\)
\(450\) −10.3256 0.687685i −0.486751 0.0324178i
\(451\) 25.7787 10.1174i 1.21387 0.476410i
\(452\) −17.0503 28.4316i −0.801977 1.33731i
\(453\) 7.31719 0.548348i 0.343792 0.0257636i
\(454\) 32.9657 + 4.68936i 1.54716 + 0.220083i
\(455\) 27.4182 3.77725i 1.28538 0.177080i
\(456\) −15.7418 + 4.00767i −0.737175 + 0.187676i
\(457\) 31.1560 + 4.69601i 1.45741 + 0.219670i 0.829454 0.558575i \(-0.188652\pi\)
0.627961 + 0.778245i \(0.283890\pi\)
\(458\) 0.0145831 + 0.0615347i 0.000681425 + 0.00287533i
\(459\) −1.02096 0.589450i −0.0476542 0.0275132i
\(460\) −15.9394 3.36078i −0.743177 0.156697i
\(461\) −6.89820 + 14.3243i −0.321281 + 0.667148i −0.997584 0.0694767i \(-0.977867\pi\)
0.676302 + 0.736624i \(0.263581\pi\)
\(462\) 21.0946 12.0556i 0.981410 0.560875i
\(463\) −22.5541 + 10.8615i −1.04818 + 0.504777i −0.877014 0.480465i \(-0.840468\pi\)
−0.171166 + 0.985242i \(0.554753\pi\)
\(464\) 3.30916 + 1.76680i 0.153624 + 0.0820217i
\(465\) −23.2718 21.5931i −1.07920 1.00136i
\(466\) 14.2764 + 29.0266i 0.661340 + 1.34463i
\(467\) 3.59533 5.27338i 0.166372 0.244023i −0.733994 0.679156i \(-0.762346\pi\)
0.900366 + 0.435133i \(0.143299\pi\)
\(468\) −11.3878 + 39.2176i −0.526403 + 1.81283i
\(469\) 2.03390 + 0.491474i 0.0939167 + 0.0226942i
\(470\) 7.28647 6.87425i 0.336100 0.317085i
\(471\) −13.7669 23.8450i −0.634345 1.09872i
\(472\) 0.953159 19.0830i 0.0438727 0.878366i
\(473\) 11.6293 7.92869i 0.534714 0.364562i
\(474\) 20.4803 36.1626i 0.940690 1.66100i
\(475\) −5.08959 1.16166i −0.233526 0.0533008i
\(476\) −0.869086 11.0205i −0.0398345 0.505122i
\(477\) 0.538539 0.122918i 0.0246580 0.00562802i
\(478\) 6.29400 21.0224i 0.287881 0.961542i
\(479\) 4.94027 + 1.52387i 0.225727 + 0.0696274i 0.405555 0.914071i \(-0.367078\pi\)
−0.179829 + 0.983698i \(0.557554\pi\)
\(480\) −23.1723 + 2.70688i −1.05767 + 0.123552i
\(481\) −34.4516 + 10.6269i −1.57086 + 0.484545i
\(482\) −12.5019 39.3675i −0.569447 1.79314i
\(483\) 5.25678 32.1050i 0.239192 1.46083i
\(484\) 8.33882 1.39877i 0.379037 0.0635806i
\(485\) −0.488165 0.191591i −0.0221664 0.00869969i
\(486\) 28.5640 + 13.4649i 1.29569 + 0.610779i
\(487\) 7.56923 1.14088i 0.342994 0.0516981i 0.0247136 0.999695i \(-0.492133\pi\)
0.318281 + 0.947996i \(0.396895\pi\)
\(488\) 0.0826086 0.226937i 0.00373952 0.0102730i
\(489\) −57.8356 −2.61542
\(490\) −13.6746 + 8.98467i −0.617757 + 0.405886i
\(491\) 33.0822i 1.49298i 0.665397 + 0.746490i \(0.268262\pi\)
−0.665397 + 0.746490i \(0.731738\pi\)
\(492\) −0.881273 53.0984i −0.0397309 2.39386i
\(493\) 0.292009 + 1.93735i 0.0131514 + 0.0872541i
\(494\) −8.78426 + 18.6347i −0.395222 + 0.838414i
\(495\) 5.06967 12.9173i 0.227865 0.580590i
\(496\) 26.0020 + 16.4912i 1.16752 + 0.740476i
\(497\) 28.0192 25.3436i 1.25683 1.13682i
\(498\) 5.84095 + 18.3926i 0.261739 + 0.824194i
\(499\) −2.64842 8.58596i −0.118559 0.384360i 0.876768 0.480913i \(-0.159695\pi\)
−0.995328 + 0.0965525i \(0.969218\pi\)
\(500\) −22.5078 8.40534i −1.00658 0.375898i
\(501\) −6.45556 + 20.9284i −0.288413 + 0.935013i
\(502\) 16.1061 + 4.82210i 0.718853 + 0.215221i
\(503\) −5.17944 22.6926i −0.230940 1.01181i −0.948862 0.315690i \(-0.897764\pi\)
0.717922 0.696123i \(-0.245093\pi\)
\(504\) −3.88911 23.8270i −0.173235 1.06134i
\(505\) −6.02969 + 26.4178i −0.268318 + 1.17558i
\(506\) −8.93741 + 15.7810i −0.397316 + 0.701552i
\(507\) 38.0330 + 55.7842i 1.68911 + 2.47746i
\(508\) −13.8240 + 4.51669i −0.613339 + 0.200396i
\(509\) −1.74626 + 1.00820i −0.0774016 + 0.0446879i −0.538201 0.842816i \(-0.680896\pi\)
0.460800 + 0.887504i \(0.347563\pi\)
\(510\) −8.36161 8.86303i −0.370258 0.392461i
\(511\) −25.5924 12.7275i −1.13214 0.563030i
\(512\) 21.6229 6.66695i 0.955608 0.294640i
\(513\) −1.07313 0.731646i −0.0473797 0.0323029i
\(514\) 10.9602 + 22.2842i 0.483435 + 0.982915i
\(515\) 20.4880 22.0809i 0.902811 0.972999i
\(516\) −6.44188 26.2109i −0.283588 1.15387i
\(517\) −4.83899 10.0483i −0.212818 0.441922i
\(518\) 15.6879 14.4283i 0.689286 0.633944i
\(519\) −23.9386 11.5282i −1.05079 0.506033i
\(520\) −16.0539 + 24.8541i −0.704010 + 1.08993i
\(521\) −12.0598 + 20.8883i −0.528352 + 0.915132i 0.471102 + 0.882079i \(0.343856\pi\)
−0.999454 + 0.0330531i \(0.989477\pi\)
\(522\) 0.986699 + 4.16346i 0.0431867 + 0.182230i
\(523\) −4.38647 + 29.1023i −0.191807 + 1.27256i 0.661022 + 0.750366i \(0.270123\pi\)
−0.852829 + 0.522190i \(0.825115\pi\)
\(524\) −12.6992 17.9779i −0.554769 0.785370i
\(525\) 4.59493 14.2514i 0.200539 0.621982i
\(526\) 0.850280 5.97737i 0.0370740 0.260626i
\(527\) 1.20177 + 16.0365i 0.0523498 + 0.698560i
\(528\) −4.93625 + 25.5006i −0.214823 + 1.10977i
\(529\) 0.469068 + 1.19516i 0.0203942 + 0.0519637i
\(530\) 0.399338 + 0.0265960i 0.0173461 + 0.00115526i
\(531\) 17.0389 13.5880i 0.739423 0.589671i
\(532\) −0.0474794 12.1790i −0.00205849 0.528026i
\(533\) −52.6574 41.9928i −2.28084 1.81891i
\(534\) −4.71948 4.30671i −0.204232 0.186370i
\(535\) −1.52238 + 20.3147i −0.0658181 + 0.878282i
\(536\) −1.81628 + 1.30571i −0.0784515 + 0.0563980i
\(537\) −4.82769 + 4.47944i −0.208330 + 0.193302i
\(538\) −10.2962 + 26.8883i −0.443902 + 1.15924i
\(539\) 4.92571 + 17.5380i 0.212165 + 0.755416i
\(540\) −1.38829 1.24591i −0.0597424 0.0536156i
\(541\) 25.6685 + 27.6640i 1.10357 + 1.18937i 0.980407 + 0.196983i \(0.0631145\pi\)
0.123167 + 0.992386i \(0.460695\pi\)
\(542\) −4.51108 0.990316i −0.193767 0.0425377i
\(543\) −2.86325 + 38.2075i −0.122874 + 1.63964i
\(544\) 9.53730 + 6.97879i 0.408908 + 0.299213i
\(545\) 14.2977 17.9287i 0.612444 0.767981i
\(546\) −51.0435 29.7702i −2.18446 1.27405i
\(547\) 9.14210 7.29058i 0.390888 0.311723i −0.408250 0.912870i \(-0.633861\pi\)
0.799138 + 0.601147i \(0.205289\pi\)
\(548\) 11.2200 + 5.17568i 0.479295 + 0.221094i
\(549\) 0.256423 0.100639i 0.0109439 0.00429515i
\(550\) −5.15028 + 6.56933i −0.219609 + 0.280117i
\(551\) 0.161306 + 2.15248i 0.00687188 + 0.0916988i
\(552\) 22.3543 + 26.6430i 0.951462 + 1.13400i
\(553\) 22.5707 + 21.4822i 0.959803 + 0.913517i
\(554\) −4.11377 2.75500i −0.174777 0.117049i
\(555\) 3.50145 23.2306i 0.148628 0.986083i
\(556\) −1.01892 + 7.61559i −0.0432118 + 0.322973i
\(557\) −29.2280 16.8748i −1.23843 0.715007i −0.269656 0.962957i \(-0.586910\pi\)
−0.968773 + 0.247950i \(0.920243\pi\)
\(558\) 5.52239 + 34.6834i 0.233781 + 1.46827i
\(559\) −30.8412 14.8523i −1.30444 0.628187i
\(560\) 2.25203 17.3463i 0.0951658 0.733015i
\(561\) −12.2224 + 5.88599i −0.516029 + 0.248507i
\(562\) −15.4833 22.3099i −0.653126 0.941086i
\(563\) 17.0810 18.4089i 0.719876 0.775842i −0.262060 0.965051i \(-0.584402\pi\)
0.981937 + 0.189209i \(0.0605924\pi\)
\(564\) −21.2978 + 1.95196i −0.896800 + 0.0821923i
\(565\) 15.4335 22.6368i 0.649293 0.952338i
\(566\) 1.81072 + 21.7401i 0.0761100 + 0.913803i
\(567\) −13.8590 + 16.9330i −0.582021 + 0.711119i
\(568\) 1.00531 + 40.3767i 0.0421820 + 1.69417i
\(569\) −3.62982 6.28704i −0.152170 0.263566i 0.779855 0.625960i \(-0.215293\pi\)
−0.932025 + 0.362394i \(0.881959\pi\)
\(570\) −8.45663 10.4256i −0.354209 0.436682i
\(571\) −17.4499 25.5943i −0.730255 1.07109i −0.994304 0.106579i \(-0.966010\pi\)
0.264049 0.964509i \(-0.414942\pi\)
\(572\) 20.9633 + 25.4104i 0.876519 + 1.06246i
\(573\) 19.5314 + 4.45791i 0.815935 + 0.186232i
\(574\) 38.7791 + 9.03074i 1.61861 + 0.376936i
\(575\) 2.48717 + 10.8970i 0.103722 + 0.454436i
\(576\) 22.0217 + 13.4596i 0.917570 + 0.560817i
\(577\) 16.1632 + 4.98568i 0.672881 + 0.207556i 0.612322 0.790608i \(-0.290235\pi\)
0.0605590 + 0.998165i \(0.480712\pi\)
\(578\) −0.148273 17.8687i −0.00616734 0.743240i
\(579\) −0.783391 2.53969i −0.0325566 0.105546i
\(580\) −0.180338 + 3.09486i −0.00748814 + 0.128507i
\(581\) −14.4409 + 0.897976i −0.599110 + 0.0372543i
\(582\) 0.567840 + 0.964948i 0.0235377 + 0.0399984i
\(583\) 0.162790 0.414782i 0.00674207 0.0171785i
\(584\) 28.1571 11.8679i 1.16515 0.491097i
\(585\) −33.3717 + 5.02998i −1.37975 + 0.207964i
\(586\) −1.16459 2.89642i −0.0481087 0.119650i
\(587\) 22.7807i 0.940259i 0.882597 + 0.470130i \(0.155793\pi\)
−0.882597 + 0.470130i \(0.844207\pi\)
\(588\) 34.8112 + 2.91696i 1.43559 + 0.120293i
\(589\) 17.7171i 0.730022i
\(590\) 14.6502 5.89054i 0.603140 0.242510i
\(591\) 24.0234 3.62095i 0.988191 0.148946i
\(592\) 0.756137 + 22.7731i 0.0310770 + 0.935967i
\(593\) −12.6676 + 32.2764i −0.520195 + 1.32543i 0.393609 + 0.919278i \(0.371227\pi\)
−0.913803 + 0.406157i \(0.866869\pi\)
\(594\) −1.78988 + 1.05329i −0.0734398 + 0.0432169i
\(595\) 7.96913 4.46704i 0.326703 0.183131i
\(596\) 27.3977 + 1.59647i 1.12225 + 0.0653939i
\(597\) −5.35461 17.3592i −0.219150 0.710466i
\(598\) 44.1067 0.365994i 1.80366 0.0149666i
\(599\) 33.4678 + 10.3234i 1.36746 + 0.421804i 0.889643 0.456657i \(-0.150953\pi\)
0.477813 + 0.878461i \(0.341429\pi\)
\(600\) 8.34644 + 13.6596i 0.340742 + 0.557650i
\(601\) 3.12538 + 13.6932i 0.127487 + 0.558557i 0.997814 + 0.0660831i \(0.0210502\pi\)
−0.870327 + 0.492474i \(0.836093\pi\)
\(602\) 20.2366 + 0.0890270i 0.824781 + 0.00362847i
\(603\) −2.48748 0.567752i −0.101298 0.0231207i
\(604\) −3.74279 4.53678i −0.152292 0.184599i
\(605\) 3.93625 + 5.77342i 0.160031 + 0.234723i
\(606\) 44.9300 36.4445i 1.82516 1.48046i
\(607\) −8.31437 14.4009i −0.337470 0.584515i 0.646486 0.762926i \(-0.276238\pi\)
−0.983956 + 0.178411i \(0.942904\pi\)
\(608\) 9.90342 + 8.45235i 0.401637 + 0.342788i
\(609\) −6.19076 0.0786084i −0.250862 0.00318537i
\(610\) 0.198894 0.0165658i 0.00805299 0.000670728i
\(611\) −15.2796 + 22.4110i −0.618146 + 0.906654i
\(612\) 1.23027 + 13.4235i 0.0497307 + 0.542612i
\(613\) −29.4487 + 31.7382i −1.18942 + 1.28189i −0.238968 + 0.971027i \(0.576809\pi\)
−0.950454 + 0.310865i \(0.899381\pi\)
\(614\) 25.6392 17.7939i 1.03471 0.718104i
\(615\) 39.5411 19.0420i 1.59445 0.767846i
\(616\) −17.6475 8.23500i −0.711040 0.331797i
\(617\) −14.1832 6.83025i −0.570993 0.274976i 0.126028 0.992027i \(-0.459777\pi\)
−0.697021 + 0.717051i \(0.745491\pi\)
\(618\) −63.5100 + 10.1122i −2.55475 + 0.406774i
\(619\) −6.65331 3.84129i −0.267419 0.154394i 0.360295 0.932838i \(-0.382676\pi\)
−0.627714 + 0.778444i \(0.716009\pi\)
\(620\) −3.37442 + 25.2210i −0.135520 + 1.01290i
\(621\) −0.414457 + 2.74974i −0.0166316 + 0.110343i
\(622\) 9.73311 14.5335i 0.390262 0.582740i
\(623\) 3.99192 2.64803i 0.159933 0.106091i
\(624\) 59.7129 20.6128i 2.39043 0.825171i
\(625\) −0.636298 8.49080i −0.0254519 0.339632i
\(626\) 7.36413 + 5.77339i 0.294330 + 0.230751i
\(627\) −13.9125 + 5.46026i −0.555612 + 0.218062i
\(628\) −9.24418 + 20.0398i −0.368883 + 0.799676i
\(629\) −9.30424 + 7.41988i −0.370984 + 0.295850i
\(630\) 16.5340 11.1665i 0.658731 0.444883i
\(631\) 12.2743 15.3915i 0.488632 0.612725i −0.474991 0.879991i \(-0.657549\pi\)
0.963623 + 0.267266i \(0.0861201\pi\)
\(632\) −33.1456 + 3.31538i −1.31846 + 0.131879i
\(633\) 3.28588 43.8470i 0.130602 1.74276i
\(634\) −2.20009 + 10.0218i −0.0873766 + 0.398017i
\(635\) −8.17474 8.81028i −0.324405 0.349625i
\(636\) −0.635933 0.570716i −0.0252164 0.0226304i
\(637\) 30.9493 31.7015i 1.22626 1.25606i
\(638\) 3.22324 + 1.23426i 0.127609 + 0.0488649i
\(639\) −33.7707 + 31.3346i −1.33595 + 1.23958i
\(640\) 12.4881 + 13.9185i 0.493634 + 0.550175i
\(641\) 2.20002 29.3572i 0.0868955 1.15954i −0.767898 0.640572i \(-0.778697\pi\)
0.854794 0.518968i \(-0.173684\pi\)
\(642\) 29.3175 32.1274i 1.15707 1.26797i
\(643\) −2.58245 2.05943i −0.101842 0.0812161i 0.571245 0.820780i \(-0.306461\pi\)
−0.673087 + 0.739563i \(0.735032\pi\)
\(644\) −23.4492 + 11.4054i −0.924029 + 0.449435i
\(645\) 17.4392 13.9073i 0.686669 0.547600i
\(646\) −0.451890 + 6.78510i −0.0177794 + 0.266956i
\(647\) 0.0279662 + 0.0712567i 0.00109946 + 0.00280139i 0.931422 0.363940i \(-0.118569\pi\)
−0.930323 + 0.366741i \(0.880473\pi\)
\(648\) −4.06109 23.0370i −0.159535 0.904979i
\(649\) −1.31373 17.5306i −0.0515686 0.688135i
\(650\) 20.0994 + 2.85914i 0.788365 + 0.112145i
\(651\) −50.6236 4.44074i −1.98409 0.174046i
\(652\) 26.7458 + 37.8633i 1.04745 + 1.48284i
\(653\) −2.91085 + 19.3122i −0.113910 + 0.755745i 0.856827 + 0.515603i \(0.172432\pi\)
−0.970738 + 0.240142i \(0.922806\pi\)
\(654\) −47.6395 + 11.2901i −1.86285 + 0.441478i
\(655\) 9.09503 15.7530i 0.355372 0.615523i
\(656\) −34.3545 + 25.1321i −1.34132 + 0.981243i
\(657\) 31.4012 + 15.1220i 1.22508 + 0.589966i
\(658\) 2.45966 15.8455i 0.0958877 0.617721i
\(659\) −14.3815 29.8635i −0.560224 1.16332i −0.968166 0.250310i \(-0.919468\pi\)
0.407942 0.913008i \(-0.366247\pi\)
\(660\) −20.8450 + 5.12309i −0.811389 + 0.199416i
\(661\) 0.560032 0.603571i 0.0217827 0.0234762i −0.722067 0.691824i \(-0.756808\pi\)
0.743849 + 0.668347i \(0.232998\pi\)
\(662\) 17.9365 8.82184i 0.697121 0.342871i
\(663\) 27.2601 + 18.5856i 1.05869 + 0.721805i
\(664\) 9.34002 12.3295i 0.362463 0.478478i
\(665\) 9.12292 4.25153i 0.353772 0.164867i
\(666\) −18.9044 + 17.8349i −0.732532 + 0.691090i
\(667\) 4.00231 2.31073i 0.154970 0.0894719i
\(668\) 16.6866 5.45199i 0.645624 0.210944i
\(669\) 23.3557 + 34.2566i 0.902985 + 1.32444i
\(670\) −1.60856 0.910989i −0.0621440 0.0351946i
\(671\) 0.0494449 0.216632i 0.00190880 0.00836299i
\(672\) −26.6333 + 26.1787i −1.02740 + 1.00987i
\(673\) −0.161867 0.709186i −0.00623952 0.0273371i 0.971712 0.236168i \(-0.0758914\pi\)
−0.977952 + 0.208831i \(0.933034\pi\)
\(674\) 4.81474 16.0816i 0.185457 0.619439i
\(675\) −0.377265 + 1.22306i −0.0145209 + 0.0470757i
\(676\) 18.9321 50.6963i 0.728158 1.94986i
\(677\) −4.07964 13.2259i −0.156793 0.508312i 0.842757 0.538294i \(-0.180931\pi\)
−0.999550 + 0.0299824i \(0.990455\pi\)
\(678\) −55.7498 + 17.7045i −2.14106 + 0.679936i
\(679\) −0.805238 + 0.237229i −0.0309022 + 0.00910402i
\(680\) −1.93558 + 9.57278i −0.0742261 + 0.367099i
\(681\) 21.4637 54.6887i 0.822492 2.09568i
\(682\) 25.6253 + 12.0796i 0.981244 + 0.462552i
\(683\) −2.59893 17.2428i −0.0994453 0.659777i −0.981903 0.189385i \(-0.939351\pi\)
0.882458 0.470392i \(-0.155887\pi\)
\(684\) 0.246445 + 14.8488i 0.00942305 + 0.567757i
\(685\) 10.2113i 0.390155i
\(686\) −8.46224 + 24.7869i −0.323090 + 0.946368i
\(687\) 0.111579 0.00425699
\(688\) −14.1805 + 16.3384i −0.540626 + 0.622897i
\(689\) −1.07158 + 0.161515i −0.0408241 + 0.00615324i
\(690\) −12.2552 + 25.9979i −0.466549 + 0.989723i
\(691\) −3.35406 1.31637i −0.127594 0.0500771i 0.300685 0.953724i \(-0.402785\pi\)
−0.428279 + 0.903646i \(0.640880\pi\)
\(692\) 3.52311 + 21.0031i 0.133929 + 0.798419i
\(693\) −6.27731 21.3074i −0.238455 0.809400i
\(694\) −35.7245 + 11.3450i −1.35608 + 0.430652i
\(695\) −6.06760 + 1.87161i −0.230157 + 0.0709941i
\(696\) 4.37972 4.96243i 0.166013 0.188100i
\(697\) −21.2438 6.55284i −0.804666 0.248206i
\(698\) −40.2633 12.0546i −1.52399 0.456274i
\(699\) 55.6426 12.7001i 2.10460 0.480360i
\(700\) −11.4549 + 3.58233i −0.432955 + 0.135399i
\(701\) 12.8938 + 2.94293i 0.486993 + 0.111153i 0.458965 0.888454i \(-0.348220\pi\)
0.0280277 + 0.999607i \(0.491077\pi\)
\(702\) 4.39502 + 2.48907i 0.165879 + 0.0939440i
\(703\) −10.8328 + 7.38570i −0.408568 + 0.278557i
\(704\) 18.9773 8.56105i 0.715234 0.322657i
\(705\) −8.83729 15.3066i −0.332832 0.576481i
\(706\) 24.8601 + 26.3509i 0.935622 + 0.991728i
\(707\) 18.3223 + 39.3159i 0.689081 + 1.47863i
\(708\) −32.3746 9.40079i −1.21671 0.353303i
\(709\) 3.40193 4.98971i 0.127762 0.187393i −0.757028 0.653383i \(-0.773349\pi\)
0.884790 + 0.465990i \(0.154302\pi\)
\(710\) −29.9515 + 14.7313i −1.12406 + 0.552855i
\(711\) −27.8524 25.8432i −1.04455 0.969197i
\(712\) −0.636980 + 5.08133i −0.0238718 + 0.190431i
\(713\) 34.1765 16.4585i 1.27992 0.616377i
\(714\) −19.2739 2.99185i −0.721309 0.111967i
\(715\) −11.8118 + 24.5274i −0.441735 + 0.917272i
\(716\) 5.16511 + 1.08905i 0.193029 + 0.0406998i
\(717\) −33.5312 19.3592i −1.25224 0.722984i
\(718\) 14.5154 3.44001i 0.541710 0.128380i
\(719\) 10.0528 + 1.51522i 0.374908 + 0.0565083i 0.333794 0.942646i \(-0.391671\pi\)
0.0411142 + 0.999154i \(0.486909\pi\)
\(720\) −2.47729 + 21.1847i −0.0923230 + 0.789508i
\(721\) 4.21348 48.0328i 0.156918 1.78884i
\(722\) 2.72908 19.1851i 0.101566 0.713997i
\(723\) −72.6742 + 5.44618i −2.70278 + 0.202546i
\(724\) 26.3374 15.7944i 0.978823 0.586994i
\(725\) 1.98009 0.777129i 0.0735388 0.0288619i
\(726\) 0.991380 14.8855i 0.0367936 0.552454i
\(727\) −5.00609 6.27744i −0.185666 0.232817i 0.680284 0.732949i \(-0.261856\pi\)
−0.865950 + 0.500131i \(0.833285\pi\)
\(728\) 4.11519 + 47.1838i 0.152519 + 1.74875i
\(729\) 19.2694 24.1631i 0.713682 0.894929i
\(730\) 18.6528 + 17.0215i 0.690372 + 0.629992i
\(731\) −11.2675 0.844383i −0.416744 0.0312306i
\(732\) −0.356003 0.234160i −0.0131582 0.00865481i
\(733\) 5.12209 + 5.52030i 0.189189 + 0.203897i 0.820522 0.571614i \(-0.193683\pi\)
−0.631334 + 0.775511i \(0.717492\pi\)
\(734\) 19.9333 + 7.63300i 0.735753 + 0.281739i
\(735\) 9.86136 + 27.1327i 0.363742 + 1.00081i
\(736\) 7.10475 26.9557i 0.261885 0.993599i
\(737\) −1.50871 + 1.39988i −0.0555742 + 0.0515653i
\(738\) −47.4221 10.4106i −1.74563 0.383218i
\(739\) −42.6607 3.19698i −1.56930 0.117603i −0.738530 0.674220i \(-0.764480\pi\)
−0.830769 + 0.556617i \(0.812099\pi\)
\(740\) −16.8276 + 8.45059i −0.618596 + 0.310650i
\(741\) 28.4186 + 22.6631i 1.04398 + 0.832550i
\(742\) 0.530916 0.358561i 0.0194905 0.0131632i
\(743\) 18.5600 + 23.2735i 0.680899 + 0.853820i 0.995437 0.0954247i \(-0.0304209\pi\)
−0.314538 + 0.949245i \(0.601849\pi\)
\(744\) 38.8922 37.9313i 1.42586 1.39063i
\(745\) 8.28602 + 21.1124i 0.303576 + 0.773499i
\(746\) −9.61377 + 12.2627i −0.351985 + 0.448968i
\(747\) 17.5935 1.31845i 0.643713 0.0482396i
\(748\) 9.50558 + 5.27969i 0.347558 + 0.193045i
\(749\) 18.0262 + 27.1746i 0.658663 + 0.992937i
\(750\) −23.5884 + 35.2223i −0.861328 + 1.28614i
\(751\) 22.5558 + 3.39974i 0.823072 + 0.124058i 0.547057 0.837095i \(-0.315748\pi\)
0.276015 + 0.961153i \(0.410986\pi\)
\(752\) 11.1270 + 13.0404i 0.405760 + 0.475535i
\(753\) 14.8319 25.6896i 0.540505 0.936183i
\(754\) −1.31992 8.28979i −0.0480688 0.301896i
\(755\) 2.10888 4.37913i 0.0767499 0.159373i
\(756\) −2.97849 0.211534i −0.108327 0.00769341i
\(757\) −3.31534 6.88437i −0.120498 0.250217i 0.831991 0.554789i \(-0.187201\pi\)
−0.952489 + 0.304572i \(0.901487\pi\)
\(758\) −25.0202 + 17.3643i −0.908773 + 0.630700i
\(759\) 23.4570 + 21.7650i 0.851437 + 0.790018i
\(760\) −2.91463 + 10.3576i −0.105725 + 0.375710i
\(761\) −16.5589 11.2897i −0.600259 0.409250i 0.224711 0.974425i \(-0.427856\pi\)
−0.824971 + 0.565176i \(0.808808\pi\)
\(762\) 2.12981 + 25.5712i 0.0771549 + 0.926347i
\(763\) 0.466066 36.7047i 0.0168727 1.32880i
\(764\) −6.11374 14.8482i −0.221187 0.537189i
\(765\) −9.64738 + 5.56992i −0.348802 + 0.201381i
\(766\) −34.6141 + 28.0768i −1.25066 + 1.01446i
\(767\) −35.3259 + 24.0848i −1.27554 + 0.869651i
\(768\) −2.64826 39.8357i −0.0955608 1.43745i
\(769\) −1.86621 + 8.17641i −0.0672973 + 0.294849i −0.997366 0.0725377i \(-0.976890\pi\)
0.930068 + 0.367387i \(0.119747\pi\)
\(770\) 0.0708013 16.0937i 0.00255150 0.579977i
\(771\) 42.7178 9.75007i 1.53845 0.351140i
\(772\) −1.30039 + 1.68734i −0.0468020 + 0.0607285i
\(773\) 0.112689 0.365328i 0.00405314 0.0131399i −0.953524 0.301318i \(-0.902573\pi\)
0.957577 + 0.288178i \(0.0930496\pi\)
\(774\) −24.6753 + 0.204753i −0.886934 + 0.00735971i
\(775\) 16.6839 5.14629i 0.599302 0.184860i
\(776\) 0.369128 0.817985i 0.0132509 0.0293640i
\(777\) −18.3881 32.8041i −0.659669 1.17684i
\(778\) −7.79230 13.2417i −0.279368 0.474737i
\(779\) −22.7996 8.94819i −0.816881 0.320602i
\(780\) 36.1386 + 37.6744i 1.29397 + 1.34896i
\(781\) 5.53859 + 36.7461i 0.198186 + 1.31488i
\(782\) 13.5083 5.43139i 0.483055 0.194226i
\(783\) 0.529213 0.0189125
\(784\) −14.1886 24.1388i −0.506737 0.862101i
\(785\) −18.2383 −0.650952
\(786\) −36.0322 + 14.4878i −1.28523 + 0.516762i
\(787\) −1.94990 12.9368i −0.0695065 0.461145i −0.996326 0.0856389i \(-0.972707\pi\)
0.926820 0.375506i \(-0.122531\pi\)
\(788\) −13.4801 14.0530i −0.480207 0.500616i
\(789\) −9.91621 3.89182i −0.353026 0.138553i
\(790\) −13.9617 23.7255i −0.496734 0.844115i
\(791\) −2.72185 43.7717i −0.0967777 1.55634i
\(792\) 21.6447 + 9.76749i 0.769109 + 0.347072i
\(793\) −0.516404 + 0.159289i −0.0183380 + 0.00565654i
\(794\) −37.4647 + 0.310879i −1.32957 + 0.0110327i
\(795\) 0.208141 0.674777i 0.00738201 0.0239319i
\(796\) −8.88838 + 11.5332i −0.315040 + 0.408784i
\(797\) −32.0982 + 7.32620i −1.13698 + 0.259507i −0.749263 0.662273i \(-0.769592\pi\)
−0.387713 + 0.921780i \(0.626735\pi\)
\(798\) −20.9287 4.87379i −0.740866 0.172530i
\(799\) −1.99228 + 8.72873i −0.0704817 + 0.308800i
\(800\) 5.08276 11.7810i 0.179703 0.416521i
\(801\) −4.82624 + 3.29047i −0.170527 + 0.116263i
\(802\) 11.4413 9.28048i 0.404006 0.327705i
\(803\) 24.3473 14.0569i 0.859199 0.496059i
\(804\) 1.50269 + 3.64952i 0.0529958 + 0.128709i
\(805\) −16.6761 13.6487i −0.587754 0.481053i
\(806\) −5.71882 68.6621i −0.201437 2.41852i
\(807\) 41.9736 + 28.6171i 1.47754 + 1.00737i
\(808\) −44.6369 12.5608i −1.57032 0.441888i
\(809\) 20.6466 + 19.1572i 0.725895 + 0.673532i 0.953899 0.300128i \(-0.0970293\pi\)
−0.228004 + 0.973660i \(0.573220\pi\)
\(810\) 15.8816 11.0221i 0.558024 0.387276i
\(811\) 3.17871 + 6.60066i 0.111620 + 0.231780i 0.949294 0.314389i \(-0.101800\pi\)
−0.837675 + 0.546170i \(0.816085\pi\)
\(812\) 2.81143 + 4.08927i 0.0986619 + 0.143505i
\(813\) −3.53565 + 7.34186i −0.124001 + 0.257490i
\(814\) 3.29651 + 20.7037i 0.115542 + 0.725665i
\(815\) −19.1550 + 33.1775i −0.670971 + 1.16216i
\(816\) 15.8619 13.5345i 0.555279 0.473803i
\(817\) −12.3093 1.85533i −0.430649 0.0649099i
\(818\) −21.8507 + 32.6275i −0.763992 + 1.14079i
\(819\) −37.2448 + 39.1319i −1.30144 + 1.36738i
\(820\) −30.7518 17.0805i −1.07390 0.596478i
\(821\) 5.48691 0.411187i 0.191495 0.0143505i 0.0213625 0.999772i \(-0.493200\pi\)
0.170132 + 0.985421i \(0.445581\pi\)
\(822\) 13.4509 17.1571i 0.469155 0.598421i
\(823\) −14.3314 36.5157i −0.499560 1.27286i −0.929106 0.369814i \(-0.879422\pi\)
0.429546 0.903045i \(-0.358674\pi\)
\(824\) 35.9902 + 36.9018i 1.25378 + 1.28554i
\(825\) 9.18297 + 11.5151i 0.319710 + 0.400903i
\(826\) 12.7341 21.8338i 0.443077 0.759694i
\(827\) 30.4056 + 24.2477i 1.05731 + 0.843175i 0.988005 0.154421i \(-0.0493511\pi\)
0.0693028 + 0.997596i \(0.477923\pi\)
\(828\) 28.4144 14.2693i 0.987470 0.495893i
\(829\) −18.6723 1.39930i −0.648516 0.0485996i −0.253589 0.967312i \(-0.581611\pi\)
−0.394927 + 0.918712i \(0.629230\pi\)
\(830\) 12.4855 + 2.74093i 0.433377 + 0.0951392i
\(831\) −6.40367 + 5.94174i −0.222141 + 0.206117i
\(832\) −41.1086 29.5601i −1.42518 1.02481i
\(833\) 5.68666 13.4730i 0.197031 0.466812i
\(834\) 12.6602 + 4.84790i 0.438385 + 0.167869i
\(835\) 9.86755 + 10.6347i 0.341481 + 0.368029i
\(836\) 10.0085 + 6.58305i 0.346150 + 0.227680i
\(837\) 4.33164 + 0.324612i 0.149723 + 0.0112202i
\(838\) 26.8051 + 24.4608i 0.925968 + 0.844984i
\(839\) 14.8712 18.6479i 0.513410 0.643796i −0.455785 0.890090i \(-0.650641\pi\)
0.969195 + 0.246294i \(0.0792129\pi\)
\(840\) −28.8645 10.9241i −0.995919 0.376918i
\(841\) 17.5328 + 21.9855i 0.604581 + 0.758120i
\(842\) 1.07845 16.1929i 0.0371659 0.558044i
\(843\) −44.6022 + 17.5051i −1.53618 + 0.602907i
\(844\) −30.2249 + 18.1257i −1.04039 + 0.623913i
\(845\) 44.5972 3.34209i 1.53419 0.114972i
\(846\) −2.75368 + 19.3581i −0.0946735 + 0.665543i
\(847\) 10.6457 + 3.43238i 0.365790 + 0.117938i
\(848\) −0.0795470 + 0.680253i −0.00273165 + 0.0233600i
\(849\) 38.0609 + 5.73675i 1.30625 + 0.196885i
\(850\) 6.52064 1.54533i 0.223656 0.0530044i
\(851\) 24.3103 + 14.0356i 0.833347 + 0.481133i
\(852\) 69.7292 + 14.7022i 2.38888 + 0.503691i
\(853\) 6.39922 13.2881i 0.219105 0.454976i −0.762224 0.647314i \(-0.775892\pi\)
0.981329 + 0.192337i \(0.0616067\pi\)
\(854\) 0.235150 0.216270i 0.00804666 0.00740060i
\(855\) −11.0575 + 5.32502i −0.378159 + 0.182112i
\(856\) −34.5907 4.33618i −1.18228 0.148208i
\(857\) −23.1167 21.4491i −0.789651 0.732689i 0.178260 0.983983i \(-0.442953\pi\)
−0.967911 + 0.251295i \(0.919144\pi\)
\(858\) 52.1549 25.6517i 1.78054 0.875736i
\(859\) −2.08452 + 3.05743i −0.0711228 + 0.104318i −0.860152 0.510037i \(-0.829632\pi\)
0.789029 + 0.614355i \(0.210584\pi\)
\(860\) −17.1694 4.98558i −0.585473 0.170007i
\(861\) 31.2825 62.9030i 1.06610 2.14373i
\(862\) −23.3829 24.7851i −0.796425 0.844184i
\(863\) 8.97267 + 15.5411i 0.305433 + 0.529026i 0.977358 0.211594i \(-0.0678654\pi\)
−0.671924 + 0.740620i \(0.734532\pi\)
\(864\) 2.24795 2.26641i 0.0764769 0.0771049i
\(865\) −14.5416 + 9.91430i −0.494429 + 0.337096i
\(866\) −47.6046 26.9603i −1.61767 0.916149i
\(867\) −30.7380 7.01574i −1.04392 0.238267i
\(868\) 20.5034 + 35.1954i 0.695932 + 1.19461i
\(869\) −29.8803 + 6.81998i −1.01362 + 0.231352i
\(870\) 5.24000 + 1.56883i 0.177653 + 0.0531883i
\(871\) 4.78312 + 1.47540i 0.162070 + 0.0499920i
\(872\) 29.4220 + 25.9672i 0.996355 + 0.879359i
\(873\) 0.978132 0.301714i 0.0331048 0.0102115i
\(874\) 15.2878 4.85495i 0.517118 0.164221i
\(875\) −21.3207 23.5715i −0.720770 0.796863i
\(876\) −8.91884 53.1699i −0.301340 1.79644i
\(877\) 28.2393 + 11.0831i 0.953574 + 0.374250i 0.790567 0.612375i \(-0.209786\pi\)
0.163006 + 0.986625i \(0.447881\pi\)
\(878\) 9.90266 21.0072i 0.334198 0.708959i
\(879\) −5.44653 + 0.820932i −0.183707 + 0.0276893i
\(880\) 12.9936 + 11.2774i 0.438014 + 0.380163i
\(881\) −14.6797 −0.494571 −0.247285 0.968943i \(-0.579539\pi\)
−0.247285 + 0.968943i \(0.579539\pi\)
\(882\) 9.93403 30.3530i 0.334496 1.02204i
\(883\) 43.1546i 1.45227i 0.687553 + 0.726134i \(0.258685\pi\)
−0.687553 + 0.726134i \(0.741315\pi\)
\(884\) −0.438845 26.4412i −0.0147599 0.889315i
\(885\) −4.15230 27.5487i −0.139578 0.926041i
\(886\) 20.0162 + 9.43552i 0.672459 + 0.316992i
\(887\) 11.3735 28.9791i 0.381884 0.973023i −0.602678 0.797984i \(-0.705900\pi\)
0.984562 0.175039i \(-0.0560051\pi\)
\(888\) 39.4053 + 7.96760i 1.32236 + 0.267375i
\(889\) −18.9859 3.10869i −0.636767 0.104262i
\(890\) −4.03363 + 1.28096i −0.135208 + 0.0429379i
\(891\) −6.34391 20.5665i −0.212529 0.689002i
\(892\) 11.6260 31.1322i 0.389269 1.04238i
\(893\) −2.90743 + 9.42565i −0.0972933 + 0.315417i
\(894\) 13.8883 46.3878i 0.464493 1.55144i
\(895\) 0.970718 + 4.25299i 0.0324475 + 0.142162i
\(896\) 29.4549 + 5.32985i 0.984020 + 0.178058i
\(897\) 17.3175 75.8729i 0.578214 2.53332i
\(898\) −4.28331 2.42580i −0.142936 0.0809501i
\(899\) −4.06662 5.96464i −0.135629 0.198932i
\(900\) 13.9112 4.54519i 0.463706 0.151506i
\(901\) −0.309783 + 0.178853i −0.0103204 + 0.00595846i
\(902\) −28.4871 + 26.8755i −0.948517 + 0.894856i
\(903\) 8.38657 34.7067i 0.279088 1.15497i
\(904\) 37.3719 + 28.3105i 1.24297 + 0.941592i
\(905\) 20.9695 + 14.2967i 0.697049 + 0.475240i
\(906\) −9.31175 + 4.57987i −0.309362 + 0.152156i
\(907\) 39.4203 42.4850i 1.30893 1.41069i 0.454835 0.890576i \(-0.349698\pi\)
0.854096 0.520116i \(-0.174111\pi\)
\(908\) −45.7290 + 11.2389i −1.51757 + 0.372975i
\(909\) −22.9486 47.6532i −0.761155 1.58056i
\(910\) −33.9832 + 19.4214i −1.12653 + 0.643812i
\(911\) −22.5683 10.8683i −0.747721 0.360084i 0.0209052 0.999781i \(-0.493345\pi\)
−0.768626 + 0.639698i \(0.779059\pi\)
\(912\) 18.5407 13.5635i 0.613945 0.449133i
\(913\) 7.11579 12.3249i 0.235498 0.407895i
\(914\) −43.3579 + 10.2754i −1.43415 + 0.339880i
\(915\) 0.0524841 0.348209i 0.00173507 0.0115114i
\(916\) −0.0515991 0.0730474i −0.00170488 0.00241355i
\(917\) −3.97384 28.8452i −0.131228 0.952551i
\(918\) 1.65060 + 0.234798i 0.0544779 + 0.00774948i
\(919\) 1.79938 + 24.0111i 0.0593561 + 0.792052i 0.944871 + 0.327442i \(0.106186\pi\)
−0.885515 + 0.464610i \(0.846195\pi\)
\(920\) 22.6875 3.99948i 0.747984 0.131859i
\(921\) −20.1173 51.2582i −0.662889 1.68901i
\(922\) 1.49414 22.4345i 0.0492070 0.738841i
\(923\) 70.6607 56.3500i 2.32583 1.85478i
\(924\) −21.3185 + 26.9474i −0.701326 + 0.886503i
\(925\) 10.1016 + 8.05572i 0.332137 + 0.264871i
\(926\) 23.8635 26.1506i 0.784204 0.859363i
\(927\) −4.39374 + 58.6304i −0.144309 + 1.92567i
\(928\) −5.27415 0.572425i −0.173132 0.0187908i
\(929\) 13.4904 12.5173i 0.442607 0.410679i −0.427133 0.904189i \(-0.640477\pi\)
0.869741 + 0.493509i \(0.164286\pi\)
\(930\) 41.9274 + 16.0551i 1.37485 + 0.526468i
\(931\) 7.35680 14.3337i 0.241109 0.469768i
\(932\) −34.0461 30.5545i −1.11522 1.00085i
\(933\) −20.9915 22.6235i −0.687231 0.740659i
\(934\) −1.93540 + 8.81612i −0.0633283 + 0.288472i
\(935\) −0.671520 + 8.96081i −0.0219611 + 0.293050i
\(936\) −5.74804 57.4662i −0.187881 1.87834i
\(937\) −32.6479 + 40.9391i −1.06656 + 1.33742i −0.128205 + 0.991748i \(0.540921\pi\)
−0.938354 + 0.345675i \(0.887650\pi\)
\(938\) −2.92801 + 0.428162i −0.0956030 + 0.0139800i
\(939\) 12.9082 10.2940i 0.421244 0.335931i
\(940\) −5.93405 + 12.8640i −0.193547 + 0.419578i
\(941\) 11.0712 4.34511i 0.360909 0.141647i −0.177956 0.984038i \(-0.556948\pi\)
0.538865 + 0.842392i \(0.318853\pi\)
\(942\) 30.6439 + 24.0244i 0.998432 + 0.782758i
\(943\) 3.91883 + 52.2931i 0.127615 + 1.70290i
\(944\) 8.81707 + 25.5421i 0.286971 + 0.831324i
\(945\) −0.872302 2.30835i −0.0283760 0.0750906i
\(946\) −11.0760 + 16.5387i −0.360112 + 0.537720i
\(947\) −5.40487 + 35.8590i −0.175635 + 1.16526i 0.711137 + 0.703053i \(0.248180\pi\)
−0.886772 + 0.462207i \(0.847058\pi\)
\(948\) −7.79412 + 58.2546i −0.253141 + 1.89202i
\(949\) −59.2143 34.1874i −1.92218 1.10977i
\(950\) 7.29102 1.16090i 0.236552 0.0376645i
\(951\) 16.3107 + 7.85481i 0.528910 + 0.254710i
\(952\) 6.95447 + 14.0017i 0.225396 + 0.453797i
\(953\) −10.1212 + 4.87413i −0.327859 + 0.157888i −0.590571 0.806986i \(-0.701097\pi\)
0.262712 + 0.964874i \(0.415383\pi\)
\(954\) −0.641780 + 0.445403i −0.0207784 + 0.0144205i
\(955\) 9.02604 9.72776i 0.292076 0.314783i
\(956\) 2.83242 + 30.9045i 0.0916069 + 0.999523i
\(957\) 3.43048 5.03159i 0.110892 0.162648i
\(958\) −7.28619 + 0.606862i −0.235406 + 0.0196068i
\(959\) 10.0283 + 12.9080i 0.323831 + 0.416820i
\(960\) 28.9768 15.7769i 0.935222 0.509197i
\(961\) −14.1269 24.4685i −0.455707 0.789308i
\(962\) 39.5982 32.1196i 1.27670 1.03558i
\(963\) −22.3996 32.8541i −0.721816 1.05871i
\(964\) 37.1734 + 45.0592i 1.19727 + 1.45126i
\(965\) −1.71636 0.391747i −0.0552515 0.0126108i
\(966\) 10.0403 + 44.8991i 0.323042 + 1.44460i
\(967\) −6.86785 30.0900i −0.220855 0.967630i −0.956836 0.290628i \(-0.906136\pi\)
0.735981 0.677002i \(-0.236721\pi\)
\(968\) −10.2036 + 6.23472i −0.327956 + 0.200392i
\(969\) 11.4650 + 3.53650i 0.368310 + 0.113609i
\(970\) 0.741611 0.00615383i 0.0238117 0.000197588i
\(971\) 0.677496 + 2.19639i 0.0217419 + 0.0704854i 0.965794 0.259312i \(-0.0834958\pi\)
−0.944052 + 0.329797i \(0.893020\pi\)
\(972\) −44.5832 2.59787i −1.43001 0.0833268i
\(973\) −5.83189 + 8.32472i −0.186962 + 0.266878i
\(974\) −9.32985 + 5.49031i −0.298948 + 0.175921i
\(975\) 13.0866 33.3442i 0.419107 1.06787i
\(976\) 0.0113339 + 0.341351i 0.000362790 + 0.0109264i
\(977\) −54.7803 + 8.25680i −1.75258 + 0.264158i −0.945344 0.326075i \(-0.894274\pi\)
−0.807232 + 0.590234i \(0.799036\pi\)
\(978\) 75.8873 30.5127i 2.42661 0.975688i
\(979\) 4.71181i 0.150590i
\(980\) 13.2027 19.0034i 0.421745 0.607041i
\(981\) 44.7603i 1.42909i
\(982\) −17.4534 43.4079i −0.556960 1.38520i
\(983\) 38.8799 5.86020i 1.24008 0.186911i 0.503936 0.863741i \(-0.331885\pi\)
0.736139 + 0.676830i \(0.236647\pi\)
\(984\) 29.1698 + 69.2066i 0.929898 + 2.20623i
\(985\) 5.87934 14.9803i 0.187331 0.477312i
\(986\) −1.40525 2.38799i −0.0447524 0.0760490i
\(987\) −26.2034 10.6700i −0.834062 0.339628i
\(988\) 1.69481 29.0853i 0.0539190 0.925328i
\(989\) 7.85593 + 25.4683i 0.249804 + 0.809845i
\(990\) 0.162836 + 19.6237i 0.00517527 + 0.623683i
\(991\) 12.0673 + 3.72227i 0.383330 + 0.118242i 0.480430 0.877033i \(-0.340480\pi\)
−0.0971000 + 0.995275i \(0.530957\pi\)
\(992\) −42.8181 7.92042i −1.35948 0.251474i
\(993\) −7.84778 34.3834i −0.249042 1.09112i
\(994\) −23.3939 + 48.0362i −0.742010 + 1.52362i
\(995\) −11.7316 2.67766i −0.371916 0.0848874i
\(996\) −17.3676 21.0518i −0.550312 0.667053i
\(997\) −20.0613 29.4246i −0.635349 0.931886i −1.00000 0.000741324i \(-0.999764\pi\)
0.364651 0.931144i \(-0.381188\pi\)
\(998\) 8.00479 + 9.86858i 0.253387 + 0.312384i
\(999\) 1.60724 + 2.78382i 0.0508508 + 0.0880763i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 392.2.z.a.109.5 648
8.5 even 2 inner 392.2.z.a.109.21 yes 648
49.9 even 21 inner 392.2.z.a.205.21 yes 648
392.205 even 42 inner 392.2.z.a.205.5 yes 648
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
392.2.z.a.109.5 648 1.1 even 1 trivial
392.2.z.a.109.21 yes 648 8.5 even 2 inner
392.2.z.a.205.5 yes 648 392.205 even 42 inner
392.2.z.a.205.21 yes 648 49.9 even 21 inner